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Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K =mn+1/m+n,m>1, the explicit forms of the complete Einstein-Kahler metrics are obtained. 相似文献
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In this paper, we compute the complete Einstein-Kähler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between −2k and −1. This is the sharp estimate.
相似文献3.
《中国科学A辑(英文版)》2005,(Z1)
In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between -2k and -1. This is the sharp estimate. 相似文献
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An WANG Wei Ping YIN 《数学学报(英文版)》2006,22(2):367-376
Let YIV be the Super-Cartan domain of the fourth type, We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(Z, W). This differential equation can be solved to give an implicit function in X. We give the generating function of the Einstein Kahler metric on YIV. We obtain the explicit form of the complete Einstein-Kahler metric on YIV for a special case. 相似文献
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第四类Caftan-Hartogs域上Bergman度量与Einstein-Kahler度量等价 总被引:1,自引:0,他引:1
In this paper,we discuss the invariaut complete metric on the Cartan-Hartogs domain of the fourth type.Firstly,we find a new invariant complete metric,and prove the equivalence between Bergman metric and the new metric;Secondly,the Ricci curvature of the new metric has the super bound and lower bound;Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound;Finally,we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type. 相似文献
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Takuji Sato 《Proceedings of the American Mathematical Society》2003,131(9):2903-2909
We obtain a non-Kähler almost Hermitian manifold of constant holomorphic sectional curvature by changing the almost complex structure in a Kähler manifold of constant holomorphic sectional curvature.
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WANG Gui-xia 《数学季刊》2007,22(4):602-606
In this paper we give the proof about the equivalence of the complete Einstein- Kahler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics. 相似文献
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把文[1]中结果推广到Reinhardt域D=D(K1K2…Kp)C(1≤p<n).即证明了从域D的任一不变Khler度量都可以导出相同的Aut(D) 相似文献
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Let HCI be the Hua construction of the first type. We describe the EinsteinKahler metric for HCI. We reduce the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X(z, w, ζ). This differential equation can be solved to give an implicit function in X(z,w,ζ). For some cases, we obtained the solution of the differential equation and the explicit forms of the complete Einstein-Kahler metrics on HCI which are the non-homogeneous domains. 相似文献
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本文对一类拟凸域E(m,n,K)给出其不变Kahler度量下的全纯截曲率的显表达式,并构造了E(m,n,K)的一个不变的完备的Kahler度量,使得它大于或等于Bergman度量,而且其全纯截曲率的上界是一个负常数,从而得到E(m,n,K)的Bergman度量和Kobayashi度量的比较定理。 相似文献
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Weiping Yin 《Journal of Mathematical Analysis and Applications》2008,339(1):295-302
Monge-Ampère equation is a nonlinear equation with high degree, therefore its numerical solution is very important and very difficult. In present paper the numerical method of Dirichlet's problem of Monge-Ampère equation on Cartan-Hartogs domain of the third type is discussed by using the analytic method. Firstly, the Monge-Ampère equation is reduced to the nonlinear ordinary differential equation, then the numerical method of the Dirichlet problem of Monge-Ampère equation becomes the numerical method of two point boundary value problem of the nonlinear ordinary differential equation. Secondly, the solution of the Dirichlet problem is given in explicit formula under the special case, which can be used to check the numerical solution of the Dirichlet problem. 相似文献
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Xin ZHAO 《数学年刊B辑(英文版)》2022,43(2):265-280
The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros. If the Bergman kernel function of this type of domain has zeros, the zero set is composed of several path-connected branches, and there exists a continuous curve to connect any two points in the non-zero set. 相似文献
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In this note, we will prove a Kähler version of Cheeger-Gromoll-Perelman's soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point. 相似文献
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A. Bonome R. Castro E. Garcí a-Rí o L. Hervella R. Vá zquez-Lorenzo 《Proceedings of the American Mathematical Society》1998,126(9):2763-2769
The authors prove the existence of Osserman manifolds with indefinite Kähler metric of nonnegative or nonpositive holomorphic sectional curvature which are not locally symmetric.